T-test (การทดสอบที - Kasetsart University
1
t-test (??????????)
????? ?????????????? ???????????????????????????????????? ????? ?????????? ????????????????????? ?????????
??????? ??? ????? ?????????????????????????????????????????????????????????? ??? ???? ????????????????? ????????????????
?????????????????????????????????????????????????????????????????????
???????????????? ?????? Parametric Statistics ??????? ?????? ????? ? t test ??? ? F test ??? ????
1. ????????? ?????? Interval Scale ??? Ratio Scale
2. ???????? distribution ??? ????????? (Normal Curve)
3. ?????????????????????????????????????????????? (Variance) ??????? ?
?????????????? 2 ?????? ??? ???????????? 2 means ?? 3 ?????????
1. One Sample test
2. Paired samples test (???? ?????????????????????????)
3. Independent test (???? ??????????????????)
?????? ???????? ?????? ?????????????????? 2 means
1. One sample test
Compare means ???? One Sample test ??? ???????? ????????????? 1 ????? ???????????? ??????????? ?????????????? ???????
?????? ? Z test ??? ? t test ???????????????????????? ????????????? ?????? ???????????????? ??? ? ????????????????
???? ???? ??????? 30 ??? ? 100 (?????? ?????????????????????????) ?????? Z test ???????????????????????????????
??????????? ?????????????????????????????????? ? ???????????????? S ?????????????????????? ?????? t test
??????????????????????? ??????? ?????????????????????????????????? ??? ???????????????????
??? ?????????????? ??????????????? 183, 152, 178, 157, 194 mmHg ?????????????? ????????????????????????? ????????
?????????? 165 mmHg ?????? ????
2. Paired sample test (???? ?????????????????????????)
Compare means ???? paired samples T test ?????? 2 ????? ?????? ??????????????? (???? ???????? ???????? ??? ? ????????
??? ????) ?? ????????????????????????????? 2 ???????????? ???????? ??? (???????? ? individual ????????) ????
2
?? 5 ????????????????????????????????????????????????????? ???? ?
??? ???????? ???????????????????????????????? ???????? ????????????????????????? ???? 2 ????? (??????????????
???????????????????????????????? ????????????? ????????)
?????
1
2
3
4
5
????
115
84
88
110
105
????
170
148
176
191
158
3. Independent test (???? ??????????????????)
Compare means ???? independent t-test ??? ???????????? sample ??????????? ???????????? ??? ??????????????? 2
??????????? ???????????? ???????? mean ?????????? ????
???? ?? ???????????????????? 2 ????? ????????????? ???? ? ?????????????????????? ?????? (????????? ??????????? ??????
???????????? ??????????????)
Group
1
2
31.8
40.2
32.5
37.3
?? ????????????????? (??.)
33
43
32.9
45
32.5
40
??????????????????????????????????????? ??????? ?????????????????????????? ???????? ?????????????????? ???????????
?????????????????? ????????????? ????????????? 1, 2 ??? 3 ??????????
1.
2.
3.
3
????????????????? ??
1. One sample test
???????????????????????????????? (
) ??????????????????????????? (
) ??? ????????? (??????????) ?????????????
????????
??? ??????? ????????????? one-tailed ????????? alternative ???
1.1 ???? ?????????????????????????????? (
??? ?
)
???? ?? ? ??????????????????????????????????????????????? ??????????????????????????????????? ??????????
?????????????? ????????????????????????????????????????? ?? ???? ? ???????
???????
N (0,1)
???????
1. ???????????????? ??????????????????????????????????????????????????????????????????????? ?????????
????????????? standard normal distribution (???????????????? ? N (0,1)
2. ???????????????????????????????????????? ????????????
3. ????????????????????????????????? (???? ?)
4
1.2 ???? ?????????????????????????????????
????????? ????????????????? ???? ???????????? ????????????? ???????????????????? ??????????????? ???????? ????
1.2.1 ??????????????????????????
??????? Z =
??? Z C test??????? ?Approximation test
? N (0,1)
????????????????
1. ???????????????? ???????????????????? ???????????????? ?????????????????????????? ????????? ????????? (???????
???? ??? ? N(0,1)
2. ???????????????????????????? ????????????
3. ????????????????????????????????????
4. ?????????????????????????? 100 ??????
????????
??????? ? ??? ??? ???? ? ??? ???? ???? ?? ? ??? 30 ??? ? ???? ? ?? ????? ? ??? ???? ???? ?? ? ??????? ? ????? ??? ? ???? ??? ?????
??????????? ??? ???????????????? ???????????????? ?????????????????? ?????????????????????????????????? ?? ??? ?????????????
???????????????? 100 ??????
1.2.2 ?????????????????????????? (n < 100) ??? t-test
??????? t =
????????????????
1. ???????????????? ??????????????????????????????????????????????????????????????????????? ?????????
5
2. ???????????????????????????? ????????????
3. ????????????????????????????????????
4. ??????????????????????????? 100
2. ????????????????? (Paired sample t test)
???? ????? ??????????? ????????????????????? ?????????? ????? ?????? urine output ???? (??? ???????) ??? urine
output ?????????????????? (??? ??????)
??????? t ?
D
sD
????? D = ?????????????????????????????????????
D = ???????????? D
d1 ??? ????????????????????????????????????????????????????
d i ? Di ? D
s
2
D
?d
?
2
i
= ?????????????????????? D
(n ? 1)
s2
s D2 ? D ??????? s2 ???????????????????????
n
??????????????????? H 0 : D ? 0
D
sD
??????? t ?
????????????????? ??????? 95 %C.L. ? D ? t 0.05 s D
?????????????????????????? ????????????????? ???
??????
?? ?
?? ?
1
2
:
N
???
??????
X11
X21
:
Xn1
?X
X12
X22
:
Xn2
?X
i1
i
X1 ?
i2
???????????
Di = Xi1-Xi2
D1=X11-X12
D2=X21-X22
:
Dn=Xn1-Xn2
?D
i
i
?X
n
i1
X2 ?
? X i2
n
?D
D?
i
n
?????????????
?????????????????????
d i ? Di ? D
d1 ? D1 ? D
d12
d 2 ? D2 ? D
d 22
:
:
d n ? Dn ? D
d n21
0
?d
i
2
i
................
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